where $\omega_r$ and $\omega_q$ are the the bare frequencies of the resonator and qubit, respectively, and where $g$ is the dipole interaction strength.

The dispersive regime occurs when the resonator and qubit is far off resonance, $\Delta \gg g$, where $\Delta = \omega_r-\omega_q$ is the detuning between the resonator and the qubit (for example $\omega_r \gg \omega_q$).

In the dispersive regime the system can be described by an effective Hamiltonian on the form

where $\chi = g^2/\Delta$ . We can view the last term as a correction of the resonator frequency that depends on the qubit state, or a correction to the qubit frequency that depends on the resonator state.

In a beautiful experiment by D. I. Schuster et al., the dispersive regime was used to resolving the photon number states of a microwave resonator by monitoring a qubit that was coupled to the resonator. This notebook shows how to simulate this kind of system numerically in QuTiP.